YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True (?,1) 2. eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True (?,1) 3. eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True (?,1) 4. eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True (?,1) 5. eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True (?,1) 6. eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True (?,1) 7. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] (?,1) 8. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] (?,1) 9. eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 10. eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 11. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] 12. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] 13. eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True (1,1) 2. eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True (1,1) 3. eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True (1,1) 4. eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True (1,1) 5. eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True (1,1) 6. eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True (1,1) 7. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] (?,1) 8. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] (1,1) 9. eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 10. eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 11. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] 12. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] 13. eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = x4 + -1*x5 p(eval_start_1) = x4 + -1*x5 p(eval_start_2) = x4 + -1*x5 p(eval_start_3) = x4 + -1*x5 p(eval_start_4) = x4 + -1*x5 p(eval_start_5) = x1 + -1*x5 p(eval_start_6) = x1 + -1*x5 p(eval_start_bb0_in) = x4 + -1*x5 p(eval_start_bb1_in) = x1 + -1*x5 p(eval_start_bb2_in) = x1 + -1*x5 p(eval_start_bb3_in) = x1 + -1*x5 p(eval_start_start) = x4 + -1*x5 p(eval_start_stop) = x1 + -1*x5 Following rules are strictly oriented: [-1 + v_x + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] eval_start_6(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v_y > -1 + v__0 + -1*v_y = eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) Following rules are weakly oriented: True ==> eval_start_start(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_0(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_0(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_1(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_1(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_2(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_2(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_3(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_3(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_4(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_4(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] ==> eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v_y >= v__0 + -1*v_y = eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] ==> eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v_y >= v__0 + -1*v_y = eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v_y >= v__0 + -1*v_y = eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_5(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v_y >= v__0 + -1*v_y = eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v_y >= v__0 + -1*v_y = eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] ==> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v_y >= v__0 + -1*v_y = eval_start_stop(v__0,v__01,v_1,v_x,v_y) * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True (1,1) 2. eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True (1,1) 3. eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True (1,1) 4. eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True (1,1) 5. eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True (1,1) 6. eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True (1,1) 7. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] (?,1) 8. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] (1,1) 9. eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 10. eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 11. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] 12. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (v_x + v_y,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] 13. eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = x4 + -1*x5 p(eval_start_1) = x4 + -1*x5 p(eval_start_2) = x4 + -1*x5 p(eval_start_3) = x4 + -1*x5 p(eval_start_4) = x4 + -1*x5 p(eval_start_5) = x1 + -1*x2 p(eval_start_6) = x1 + -1*x2 p(eval_start_bb0_in) = x4 + -1*x5 p(eval_start_bb1_in) = x1 + -1*x2 p(eval_start_bb2_in) = x1 + -1*x2 p(eval_start_bb3_in) = x1 + -1*x2 p(eval_start_start) = x4 + -1*x5 p(eval_start_stop) = x1 + -1*x2 Following rules are strictly oriented: [-1 + v_x + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v__01 > -1 + v__0 + -1*v__01 = eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] eval_start_6(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v__01 > -1 + v__0 + -1*v__01 = eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) Following rules are weakly oriented: True ==> eval_start_start(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_0(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_0(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_1(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_1(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_2(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_2(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_3(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_3(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_4(v__0,v__01,v_1,v_x,v_y) True ==> eval_start_4(v__0,v__01,v_1,v_x,v_y) = v_x + -1*v_y >= v_x + -1*v_y = eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] ==> eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v__01 >= v__0 + -1*v__01 = eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] ==> eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v__01 >= v__0 + -1*v__01 = eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v__01 >= v__0 + -1*v__01 = eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 ==> && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_5(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v__01 >= v__0 + -1*v__01 = eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] ==> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) = v__0 + -1*v__01 >= v__0 + -1*v__01 = eval_start_stop(v__0,v__01,v_1,v_x,v_y) * Step 4: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True (1,1) 2. eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True (1,1) 3. eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True (1,1) 4. eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True (1,1) 5. eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True (1,1) 6. eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True (1,1) 7. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] (?,1) 8. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] (1,1) 9. eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 10. eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 11. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (v_x + v_y,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] 12. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (v_x + v_y,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] 13. eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True (1,1) 2. eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True (1,1) 3. eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True (1,1) 4. eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True (1,1) 5. eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True (1,1) 6. eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True (1,1) 7. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] (1 + 2*v_x + 2*v_y,1) 8. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] (1,1) 9. eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (1 + 2*v_x + 2*v_y,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 10. eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (1 + 2*v_x + 2*v_y,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 11. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (v_x + v_y,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] 12. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (v_x + v_y,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] 13. eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))